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Zeta and L-Functions of Varieties and Motives

2020-05-07 Mathematics
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Release : 2020-05-07
Genre : Mathematics
Kind : eBook
Book Rating : 912/5 ( reviews)

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Book Synopsis Zeta and L-Functions of Varieties and Motives by : Bruno Kahn

Download or read book Zeta and L-Functions of Varieties and Motives written by Bruno Kahn. This book was released on 2020-05-07. Available in PDF, EPUB and Kindle. Book excerpt: The amount of mathematics invented for number-theoretic reasons is impressive. It includes much of complex analysis, the re-foundation of algebraic geometry on commutative algebra, group cohomology, homological algebra, and the theory of motives. Zeta and L-functions sit at the meeting point of all these theories and have played a profound role in shaping the evolution of number theory. This book presents a big picture of zeta and L-functions and the complex theories surrounding them, combining standard material with results and perspectives that are not made explicit elsewhere in the literature. Particular attention is paid to the development of the ideas surrounding zeta and L-functions, using quotes from original sources and comments throughout the book, pointing the reader towards the relevant history. Based on an advanced course given at Jussieu in 2013, it is an ideal introduction for graduate students and researchers to this fascinating story.

Zeta and L -functions in Number Theory and Combinatorics

2019-03-01 Combinatorial number theory
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Release : 2019-03-01
Genre : Combinatorial number theory
Kind : eBook
Book Rating : 005/5 ( reviews)

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Book Synopsis Zeta and L -functions in Number Theory and Combinatorics by : Wen-Ching Winnie Li

Download or read book Zeta and L -functions in Number Theory and Combinatorics written by Wen-Ching Winnie Li. This book was released on 2019-03-01. Available in PDF, EPUB and Kindle. Book excerpt: Zeta and L-functions play a central role in number theory. They provide important information of arithmetic nature. This book, which grew out of the author's teaching over several years, explores the interaction between number theory and combinatorics using zeta and L-functions as a central theme. It provides a systematic and comprehensive account of these functions in a combinatorial setting and establishes, among other things, the combinatorial counterparts of celebrated results in number theory, such as the prime number theorem and the Chebotarev density theorem. The spectral theory for finite graphs and higher dimensional complexes is studied. Of special interest in theory and applications are the spectrally extremal objects, called Ramanujan graphs and Ramanujan complexes, which can be characterized by their associated zeta functions satisfying the Riemann Hypothesis. Explicit constructions of these extremal combinatorial objects, using number-theoretic and combinatorial means, are presented. Research on zeta and L-functions for complexes other than graphs emerged only in recent years. This is the first book for graduate students and researchers offering deep insight into this fascinating and fast developing area.

Advanced Analytic Number Theory: L-Functions

2005 Mathematics
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Release : 2005
Genre : Mathematics
Kind : eBook
Book Rating : 668/5 ( reviews)

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Book Synopsis Advanced Analytic Number Theory: L-Functions by : Carlos J. Moreno

Download or read book Advanced Analytic Number Theory: L-Functions written by Carlos J. Moreno. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of L-functions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, L-functions have assumed a greater role in the study of the interplay between Diophantine questions about primes and representation theoretic properties of Galois representations. This book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and non-vanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of Artin-Hecke and automorphic L-functions is also given. The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of L-functions and their applications in number theory and in the theory of automorphic representations. The requirements for a profitable study of this monograph are a knowledge of basic number theory and the rudiments of abstract harmonic analysis on locally compact abelian groups.

The Riemann Zeta-Function

2011-05-03 Mathematics
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Release : 2011-05-03
Genre : Mathematics
Kind : eBook
Book Rating : 146/5 ( reviews)

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Book Synopsis The Riemann Zeta-Function by : Anatoly A. Karatsuba

Download or read book The Riemann Zeta-Function written by Anatoly A. Karatsuba. This book was released on 2011-05-03. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Zeta and L Functions

1969
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Release : 1969
Genre :
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Zeta and L Functions by : Jean-Pierre Serre

Download or read book Zeta and L Functions written by Jean-Pierre Serre. This book was released on 1969. Available in PDF, EPUB and Kindle. Book excerpt:

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